0=Xcos(X)-X

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Solution for 0=Xcos(X)-X equation:


Simplifying
0 = Xcos(X) + -1X

Multiply cosX * X
0 = cosX2 + -1X

Reorder the terms:
0 = -1X + cosX2

Solving
0 = -1X + cosX2

Solving for variable 'X'.
Remove the zero:
X + -1cosX2 = -1X + cosX2 + X + -1cosX2

Reorder the terms:
X + -1cosX2 = -1X + X + cosX2 + -1cosX2

Combine like terms: -1X + X = 0
X + -1cosX2 = 0 + cosX2 + -1cosX2
X + -1cosX2 = cosX2 + -1cosX2

Combine like terms: cosX2 + -1cosX2 = 0
X + -1cosX2 = 0

Factor out the Greatest Common Factor (GCF), 'X'.
X(1 + -1cosX) = 0

Subproblem 1

Set the factor 'X' equal to zero and attempt to solve: Simplifying X = 0 Solving X = 0 Move all terms containing X to the left, all other terms to the right. Simplifying X = 0

Subproblem 2

Set the factor '(1 + -1cosX)' equal to zero and attempt to solve: Simplifying 1 + -1cosX = 0 Solving 1 + -1cosX = 0 Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1cosX = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1cosX = 0 + -1 -1cosX = 0 + -1 Combine like terms: 0 + -1 = -1 -1cosX = -1 Divide each side by '-1cos'. X = c-1o-1s-1 Simplifying X = c-1o-1s-1

Solution

X = {0, c-1o-1s-1}

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